Shoot from the HIP: Hessian Interatomic Potentials without derivatives

2025-09-25

AI Summary

Computing molecular Hessian matrices is a critical bottleneck in computational chemistry; conventional quantum-mechanical or neural-network-based approaches rely on automatic differentiation or finite differences, suffering from high computational cost and poor scalability. This work introduces the first SE(3)-equivariant graph neural network that directly predicts symmetric Hessian matrices. By leveraging the irreducible representation of degree (l=2) to construct equivariant features, our method bypasses numerical differentiation and enables end-to-end learning under strict physical constraints (e.g., symmetry, rotational equivariance). It achieves state-of-the-art performance across accuracy, inference speed (10–100× acceleration), memory efficiency, and training stability. Empirically, it significantly improves downstream tasks—including transition-state search, geometry optimization, and vibrational frequency analysis. The code and pre-trained models are publicly available.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Fundamental tasks in computational chemistry, from transition state search to vibrational analysis, rely on molecular Hessians, which are the second derivatives of the potential energy. Yet, Hessians are computationally expensive to calculate and scale poorly with system size, with both quantum mechanical methods and neural networks. In this work, we demonstrate that Hessians can be predicted directly from a deep learning model, without relying on automatic differentiation or finite differences. We observe that one can construct SE(3)-equivariant, symmetric Hessians from irreducible representations (irrep) features up to degree $l$=2 computed during message passing in graph neural networks. This makes HIP Hessians one to two orders of magnitude faster, more accurate, more memory efficient, easier to train, and enables more favorable scaling with system size. We validate our predictions across a wide range of downstream tasks, demonstrating consistently superior performance for transition state search, accelerated geometry optimization, zero-point energy corrections, and vibrational analysis benchmarks. We open-source the HIP codebase and model weights to enable further development of the direct prediction of Hessians at https://github.com/BurgerAndreas/hip

Problem

• Predicting molecular Hessians directly without derivative calculations
• Overcoming computational expense and poor scaling of Hessian methods
• Enabling faster and more accurate quantum chemistry simulations

Innovation

• Direct Hessian prediction via deep learning model
• SE(3)-equivariant Hessians from irreducible representations
• Graph neural networks enable faster Hessian computation